# Total energy non-conservation for explicit time dependent potentials

• brotherbobby

#### brotherbobby

I read from a book that the "total energy is not preserved when the potential depends explicitly on time", i.e. U(x,t). Can anyone show or prove it?

Many thanks.

Total energy will be conserved. What happens is that you will be spending some energy in changing the potential U.

For instance, consider the potential energy of some test charge, T, placed near some charged particle, A. Of course the potential energy of T will change if you move particle A around. So, in that sense, the test charge's energy is changing. But anything you lose or gain will be covered by the energy used in moving particle A.

## 1. What is total energy non-conservation for explicit time dependent potentials?

Total energy non-conservation for explicit time dependent potentials is a phenomenon in which the total energy of a system is not conserved over time. This can occur when the potential energy of the system is explicitly dependent on time, causing fluctuations in the total energy.

## 2. How does total energy non-conservation affect the accuracy of simulations?

Total energy non-conservation can significantly impact the accuracy of simulations, as it can lead to incorrect predictions and results. This is because the total energy of a system is an important parameter that determines its behavior, and any deviations from its expected value can produce inaccurate results.

## 3. What are some common causes of total energy non-conservation in simulations?

There are several potential causes of total energy non-conservation in simulations, including numerical errors, insufficient time resolution, and inconsistencies in the potential energy function. It is important to carefully analyze and address these sources of error in order to minimize the effects of total energy non-conservation.

## 4. Can total energy non-conservation be completely eliminated in simulations?

No, it is not always possible to completely eliminate total energy non-conservation in simulations. However, it can be minimized by using appropriate numerical methods, increasing time resolution, and carefully choosing potential energy functions that are as consistent as possible.

## 5. How can total energy non-conservation be detected in simulations?

Total energy non-conservation can be detected by monitoring the total energy of the system over time. If the total energy is not conserved, it will exhibit fluctuations or a gradual increase or decrease. Additionally, comparing results from different simulation methods or with experimental data can also help identify discrepancies caused by total energy non-conservation.